A complete guide is written by Maki from doshdosh.com website. Will explain you how to make a custom Google Search Engine for you website. All what you need is simply a wordpress website and Adsense account. I will post the first steps here and the rest you can read from doshdosh.com.
1. Create a Webpage for Custom Search
Start first by creating a web page on your domain for the search results page. If you are on WordPress, simply click on ‘Write’ and then select ‘Write Page’. Name the page by using ‘Search results’ or something similar as the Page title.
Leave the text box blank and publish or save the page. Note down the URL for the webpage as you will need to use it later.